Fuzzy inference relation based on the theory of falling shadows

Abstract

In this paper, we establish a theoretical approach to define a fuzzy inference relation based on the theory of falling shadows. The main characteristic of our definition of fuzzy inference relation is that it is semantically dependent in the sense that the formula of our definition will vary according to the correlation of the antecedent and the consequence of the given implication. We shall show that the formulae of fuzzy inference relation given by Łukasiewicz, Zadeh and the probability formula are consequences of our definition under three different correlations of the propositions. © 1993.